Infrared based core body temperature sensing system and method

ABSTRACT

A non-invasive and a non-contact core body temperature monitoring method and system including an infrared camera, a processor, and a non-transitory computer readable medium with a program for analyzing thermal images of the human eye. The method for using the system that includes isolating ocular thermal images from a facial image; extracting thermal information about the surface of the eye; transitioning the thermal information to a selected model of the eye; estimating a temperature at the back of the eye; optimizing the estimated temperature at the back of the eye, and transmitting the optimized temperature information to an output device.

FIELD OF THE INVENTION

The present invention generally relates to measurement of bodytemperature, specifically, core body temperature based on measuredtemperature on the ocular surface together with a heat transfer model torecover the core temperature behind the eye.

BACKGROUND OF THE INVENTION

Body temperature is one of the most important and oldest indices ofhuman physiological condition. While body temperature varies from personto person and from time to time, the human body manages to maintain arelatively constant core temperature in a range of about 36.8 to 37.7°C. through the physiological process called thermoregulation.

Surface body temperatures are known to deviate from core bodytemperature with a high degree of variation based on individual bodycharacteristics and the location on the body where the temperature ismeasured. Core body temperature is recognized as a more accurateindicator of physiological condition of the body than surface bodytemperature measurements.

Accurate monitoring of core body temperature typically requires invasivemeasurement at different sites, i.e. inserting catheters equipped withthermometers pulmonary artery, esophagus, bladder, rectum, nasopharynx,and temporal artery. However, these measurements are limited by theinconvenient operational settings of the probes. For example, apulmonary artery catheter is considered by many health practitioners tobe the most accurate measurement of core body temperature. A temperaturesensor mounted on the pulmonary artery catheter is inserted into thepulmonary artery and measures the temperature of the blood flowing fromthe heart to the lung. However, this procedure is very invasive and isassociated with some risks and complications.

Other invasive methods such as rectal probes and urinary catheter havemeasurement disparity compared with other measurement methods. Forinstance, rectal temperature is often higher than the temperaturemeasured at different site, and it is also known for its slow responseto temperature changes. The bladder (urinary) temperature measurement isconsidered accurate but has a tendency to be influenced by the amount ofthe urine flow. Other additional concerns include the risk ofperforation of the tissue during insertion of the probe/catheter andinaccurate measurement due to the displacement or detachment of thetemperature sensors.

Noninvasive temperature measurement is another method used in monitoringcore body temperature. The most widely used methods are the infraredradiation ear device (IRED), infrared thermography, and oral probes.These methods, however, are known for their lack of accuracy andconsistency. For instance, differences are observed between left andright ears, IRED has poor measurement repeatability, and its measurementaccuracy can be greatly impacted by operator technique, patient anatomy(measurement site), positioning of the probe in the ear canal, and thesensitivity of the probe to detect radiation emitted from both thetympanic membrane and the aural canal.

Another type of infrared thermometer commonly used for core bodytemperature measurement is the forehead scanning probe. The accuracy ofthe probe has shown a favorable outcome in children; however, the probeaccuracy has shown to be affected by the environmental conditions andphysical factors such as sweating, exposing to freezing or warmenvironment, or fluctuating body mass.

Temperature screening of the inner canthus of the eye is considered asthe most suitable location for remotely monitoring core bodytemperature. As a result, the measurement site has been used in massscreening during infectious disease outbreaks, such as SARS (SevereAcute Respiratory Syndrome), avian influenza, Ebola, COVID-19 etc. Eventhough the inner canthus of the eye is the most consistently warmestpart of the facial surface, the measurement has proven to beinconsistent and the number of thermal pixels captured from the innercanthus may not be adequate enough to indicate the small temperaturedifference between a healthy individual and someone with a fever.

Another noninvasive technique is a zero-heat-flux thermometry, which isused for deep tissue temperature monitoring. Even though it is easy tooperate and provides continuous measurements, the accuracy of themeasurement depends on a tight adhesion of a temperature probe to theskin, skin perfusion, and physiological changes. Small air gaps betweenthe temperature probe and the skin surface are known to reduce theaccuracy of the temperature measurement.

A shortcoming of existing core body temperature methods is the need forphysical contact with the body, which may increase the chance oftransmission of a disease between patient and clinician.

Even without physical contact, a shortcoming of measuring core bodytemperature based on the surface skin temperature (forehead, temporallobe, arms) or tear duct regions is that the temperatures of theseregions are easily affected by environmental conditions, physicalexercise, and physiological conditions.

Another shortcoming of existing core body temperature methods when usedin the context of estimating time of death is that they use muscle andrectal tissues where temperature plateau phenomena increase error indetermining the time of death.

Another shortcoming of existing core body temperature methods is slowresponse to temperature changes in the body or requiring preplanning inimplementation of the temperature measurement technique.

Another shortcoming of existing core body temperature methods is thelevel of invasiveness and inconvenience for the invasive methods, andmeasurement accuracy and repeatability for the noninvasive methods.

Therefore, an unmet need exists for a core body temperature method andsystem that does not require physical contact with the patient, providesreliable postmortem time information, and can monitor rapid changes incore body temperature without preplanning.

SUMMARY OF THE DISCLOSURE

The present invention is a system and method for measuring core bodytemperature. Specifically, estimating a core body temperature at theback of the eye based on a measurement of the ocular surface using aninfrared thermal camera directed to the eye.

One embodiment of the present disclosure is an infrared temperatureestimating method including the steps of: localization of the ocularsurface in the thermal image; transitioning temperature data from athermal image of an ocular surface of an eye to an ocular surface of afinite element mesh of the eye model; and estimating a core bodytemperature at the back of the eye model. The method may further includethe step of: transmitting the estimated core body temperature to anoutput device. The method may further include the steps of: mappingmethod between optical and thermal images; obtaining the thermal imageof the ocular surface of the eye; and extracting the temperature datafrom the thermal image of the ocular surface using knowledge of thecamera's response. The method may further include the steps of:detecting at least part of a facial surface comprising the ocularsurface of the eye; acquiring a facial thermal image of the at leastpart of the facial surface; and transmitting the facial thermal image tothe processor, where the facial thermal image comprises the thermalimage of the ocular surface of the eye. The estimating step may includeusing models of heat transfer to map between core temperature andtemperatures on the ocular surface; and performing a gradient-based ornon-gradient-based optimization procedure to estimate the core bodytemperature at the back of the eye that produces the ocular surfacetemperature profile that best fits the data according to some meritfunction. The transition step may include applying temperature data frompixel positions of the thermal image of the ocular surface of the eye to3D Cartesian coordinates on the ocular surface of a mesh or otherdiscretized model of the eye's geometry. The method may further includethe step of: constructing the model of the eye based on thermophysicalproperties and boundaries of a cornea, an anterior humor, a vitreoushumor, a lens, a retina, a choroid, an iris, a ciliary body, and asclera of an eye. In some embodiments, the core temperature may beestimated using the weak equation:

${{\int_{R}{\left( {k_{eff} + k_{i}} \right){{\nabla w} \cdot {\nabla{TdR}}}}} + {\int_{\Gamma_{u} = {\Gamma_{2}\bigcup\Gamma_{3}}}{{w\left\lbrack {{h_{\infty}\left( {T - T_{\infty}} \right)} + {\sigma {ɛ\left( {T^{4} - T_{\infty}^{4}} \right)}} + E_{v}} \right\rbrack}d\Gamma_{u}}} + {\int\limits_{\Gamma_{1}}{{{wh}_{b}\left( {T - T_{d\; \_ \; {core}}} \right)}d\Gamma_{1}}} - {\int\limits_{R}{wQ_{eff}dR}}} = {{0\mspace{11mu} {\forall{w \in {H^{1}\mspace{14mu} i}}}} = {2\mspace{11mu} \ldots \mspace{11mu} 5}}$

where H^(L) is the Sobolev space of weakly once-differentiablefunctions, k_(eff) is the effective value of the thermal conductivity ofeye tissue, k_(i) is the thermal conductivity of eye tissue in region i,w is the test function such that w∈C^(n)(R) (C^(n) is a continuousfunction of n derivatives and R is the eye domain such that R∪

^(d)) Γ₁ is part of the eye surface that is not exposed to thesurrounding air, and Γ₂∪Γ₃ is part of the eye surface that is exposed tothe surrounding air, T is the ocular surface temperature at Γ₂∪Γ₃ andthe estimated core body temperature (the surface temperature at the backof the eye) at Γ₁, T_(∞) is ambient temperature, ε is emissivity, σ isthe Boltzmann constant, E_(v) is tear evaporative heat flux, Q_(eff) isthe effective volumetric heat generation rate due to metabolism,T_(d_core) is the default core body temperature (typically set by theuser), h_(∞) is convective heat transfer coefficient between the tearfilm and the surrounding air, and h_(b) is the convective heat transfercoefficient between the vascular region (R₁) and the surrounding blood.

Another embodiment of the present disclosure may include a system forestimating a core body temperature, including: a non-transitorycomputer-readable medium in communication with a processor andcomprising a program that, when executed, performs a method, the methodincluding: transitioning temperature data from a thermal image of anocular surface of an eye to the ocular surface of a model of the eye;and estimating the core body temperature at the back of the eye model.The system may include an infrared camera in communication with theprocessor. The system may include an output device in communication withthe processor.

Examples of the more important features of the disclosure have beensummarized rather broadly in order that the detailed description thereofthat follows may be better understood and in order that thecontributions they represent to the art may be appreciated. There are,of course, additional features of the disclosure that will be describedhereinafter and which will form the subject of the claims appendedhereto.

BRIEF DESCRIPTION OF THE DRAWINGS

The organization and manner of the structure and operation of theinvention, together with further objects and advantages thereof, maybest be understood by reference to the following description taken inconnection with the accompanying drawings wherein like referencenumerals identify like elements in which:

FIG. 1 is a diagram of a system for estimating core body temperatureusing a thermal image according to one embodiment of the presentdisclosure.

FIG. 2 is a thermal image prepared using the system of FIG. 1.

FIG. 3 shows a flow chart of a method of estimating core bodytemperature according to one embodiment of the present disclosure.

FIG. 4A is a diagram of the temperature data of the eye being applied toa model of an ocular surface of the eye according to one embodiment ofthe present disclosure.

FIG. 4B is a diagram of the application of the temperature data beingapplied to the model of the eye surface according to one embodiment ofthe present disclosure.

FIG. 5 is a diagram of an adult human eye model depicting the differentregions considered in the formulating the mathematical model;

FIG. 6A is a diagram of the boundary layers of the eye model as seenfrom the front according to one embodiment of the present disclosure;

FIG. 6B is a diagram of the boundary layers of the eye model of FIG. 6Aas a side cross-section.

DETAILED DESCRIPTION OF THE DISCLOSURE

While this invention may be susceptible to embodiment in differentforms, specific embodiments are shown in the drawings and will bedescribed herein in detail with the understanding that the presentdisclosure is to be considered an exemplification of the principles ofthe invention and is not intended to limit the invention to that asillustrated.

FIG. 1 shows a system 100 for monitoring the core body temperature of ahuman body remotely. The system includes optical (visible light) andinfrared cameras 110 that can be used to acquire optical and thermalimages of an ocular surface 160 of a human, respectively. The thermalimage of the ocular surface may be a part of a thermal image of a facialsurface 150 or of a thermal image of one or both eyes. In someembodiments, the optical image of one or both eyes may be derived fromthe image of the facial surface 150. The system 100 includes a processor120 in communication with the optical and infrared cameras 110 andconfigured to receive the thermal image data. The processor 120 may bein communication with a memory 130 storing a program that, whenexecuted, may perform a method to process the thermal image data. Thememory 130 may be a non-transitory, computer readable medium, as wouldbe understood by a person of ordinary skill in the art. The system 100may also include an output device 140, such as a monitor, a transmitter,a memory, or a printer, for receiving information containing the corebody temperature estimated by the processor 120 through the execution ofthe program on the memory 130. FIG. 2 shows a facial thermal image 250,corresponding to the facial surface 150, and ocular surface thermalimages 260, corresponding to the ocular surfaces 160.

FIG. 3 shows a method 300 of estimating a core body temperatureaccording to one embodiment of the present disclosure. In step 310, atleast part of the facial surface 150 including at least one ocularsurface 160 may be detected by the optical and infrared cameras 110. Instep 320, the facial thermal image 250 may be acquired by the infraredcamera 110.

In step 330, the facial thermal image 250 may be transmitted from theinfrared camera 110 to the processor 120. In step 340, the processor120, executing the program on the memory of a local machine or cloudcomputer 130, may extract the thermal image of the right eye 260 rand/or the left eye 2601. Step 340 may be performed automatically or maybe manually performed by a person controlling the isolation of theocular surface thermal images 260 of one or both eyes. In someembodiments, step 340 may include facial feature detection where faciallandmarks are identified to localize and isolate the eye regions 260from the facial thermal image 250. The processor 120 may first identifythe location of a face from the image 250 transferred from the infraredcamera 110 using one or more of: Haar cascades, pre-trained Histogram ofOriented Gradients and Linear and support vector machine objectdetector, and deep learning-based algorithms. Once the location of theface is confirmed, then the processor 120 may execute a program forfacial landmark detection to first identify eye regions, and, then,isolate the ocular surface thermal image 260 from the facial thermalimage 250. The facial landmark detection may be based on pre-trainedfacial landmark images where ensemble regression trees are trained toestimate the facial landmark positions directly from pixel intensities.The facial landmark detection may be performed using a location of 68(x, y) coordinate points iBUG 300-W dataset. The use of the iBug-Wdataset is exemplary and illustrative only, as other suitable datasetsknown to persons of skill in the art may also be used, such as a 194coordinate points HELEN dataset. The facial landmark detector may alsobe equipped with eye blink detection feature, where it can distinguishopen eyes from closed once. The purpose of the blink feature is to trackthe eyes and facilitate automatic capture of the ocular surface imagesfrom open eyes from a recorded or live streaming infrared thermal image.

In step 345, one of the optical image and the thermal image is mappedonto the other in order to correct for differences (image sizes,mounting orientations, fields of view, etc.) due to multiple cameras 110being used to capture the optical and thermal images. This step isoptional and may not be necessary when using a single camera that cancapture both optical and infrared images. Once step 345 is complete,future performance of the method 300 may use the mapping informationfrom previous performances, thus, step 345, if needed, is only performedonce per set up of the cameras 110. Ocular landmark points (pixellocations) in the optical images may be used as a reference points tolocate the ocular landmark points in the thermal images. This mappingprocess may use homography or geometric-based mapping.

Homography mapping is performed by selecting 4-8 points in the opticalimage and the corresponding thermal image to set up an initial pixelcorrespondence between the two cameras 110. Then a homograph may beconstructed based on those data points that can then be used to mappixel locations in the optical image onto the thermal image.Geometric-based mapping is performed by using the inner canthi locationsin both the optical and thermal images as anchor points (or fixed pointsof reference). In the thermal image, the inner canthi are mostconsistently warmest part of the facial surface; hence, differentmethods can be used to locate the inner canthi, such as 1) a localizedsearch of the pixels around the eye region with the warmest temperaturevalues and 2) use of machine learning to identify location of the innercanthi. In the optical image, the location of the inner canthi may beobtained from the ocular landmark points. Following the localization ofthe inner canthi, the geometry of both images and the relationshipbetween the image dimensions and Field of Views of the chosen camerasmay then be used to map the ocular landmark points from the opticalimage onto the thermal image. Both homography and geometric basedmapping require that the cameras 110 be in close proximity to each otherduring the taking of the optical and thermal images, usually between 0.5and 2.5 inches, in order to reduce the effect of parallax.

In step 350, temperature data may be extracted from the ocular surfacethermal images 260 of the one or both eyes. Temperature data extractionmay include filtering temperature values within segmented regions of theocular surface 160.

In step 360, a model 400 of the eye may be constructed with theconsiderations of different regions: cornea, anterior and vitreoushumor, lens, retina, choroid, iris, ciliary body, and sclera, groupedbased on their thermophysical properties. In some embodiments, step 360may be optional, especially if the eye model 400 has been previouslyconstructed or provided. The eye model 400 selected to be used toestablish boundary conditions may differ based on the patient. Differentsizes of eye models, ranging from an infant to an adult size, may beconstructed using CAD and meshing software. The goal is to approximatelymatch the eyeball sizes of different age groups for an accurate estimateof core body temperature. The globes of the eye models are assumed to beaxisymmetric with respect to the optical axis. The anterior andposterior regions of the eye 500 are composed of vascular and avasculartissue structures (See FIG. 5), where the avascular part of the eye iscomposed of cornea 520, anterior chamber (aqueous humor) 530, lens 540,and vitreous humor 550, and the vascular structure 510 is composed ofretina & choroid 514, iris & ciliary body 516, and sclera 512. Due tosimilarities in thermophysical properties, an eye model may beconstructed by summarizing or using representative structures of the eyefor arrive at an eye model using five regions—R₁-R₅ in Table 1. Thethermophysical properties and other parameters of the eye model 400 areobtained from a wide range of literature and are expressed asstatistical values (i.e., mean±SD).

TABLE 1 Thermophysical properties of eye tissues (see FIG. 5) ThermalEye conductivity, Specific heat, Density, ρ Regions Tissue k [W/m-K]C_(p) [J/kg-K] [kg/m³] R₁ Sclera/Retina/ 1.0042 ± 0.04  4200 1032Iris/Choroid R₂ Cornea 0.58 ± 0.06 3515 1052 R₃ Aqueous 0.58 ± 0.01 39971003 R₄ Lens 0.43 ± 0.05 3133 1076 R₅ Vitreous 0.59 ± 0.01 4047 1005Blood 0.53 ± 0.04 3617 1050

Temperature distribution within the eye may be formulated using anenergy equation where the vascular region of the eye includes two energyequations, while the avascular region is treated as a solid tissue. Inthe vascular region 510 of the eye (R₁), for blood:

$\begin{matrix}{{{{\nabla\left( {\phi \; k_{b}{\nabla T_{b}}} \right)} + {h_{tb}{a_{tb}\left( {T_{s} - T_{b}} \right)}}} = {{\phi\rho}_{b}{c_{p_{b}}\left( {\frac{\partial T_{b}}{\partial t} + {{\overset{\rightarrow}{v}}_{b}\ {\nabla T_{b}}}} \right)}}},{{in}\mspace{14mu} R_{1}}} & (1)\end{matrix}$

For tissue:

$\begin{matrix}{{{{\nabla{\cdot \left( {\left( {1 - \phi} \right)k_{s}{\nabla T_{s}}} \right)}} + {\left( {1 - \phi} \right)Q_{m}} + {h_{tb}{a_{tb}\left( {T_{b} - T_{s}} \right)}}} = {\left( {1 - \phi} \right)\rho_{s}c_{p_{s}}\frac{\partial T_{s}}{\partial t}}},{{in}\mspace{14mu} R_{1}}} & (2)\end{matrix}$

In the avascular region 520, 530, 540, 550 of the eye (R_(i)):

$\begin{matrix}{{{\nabla{\cdot \left( {k_{i}{\nabla T_{i}}} \right)}} = {\rho_{i}c_{p_{i}}\frac{\partial T_{i}}{\partial t}}},{{in}\mspace{14mu} R_{i}},{i = {2\mspace{14mu} \ldots \mspace{11mu} 5}}} & (3)\end{matrix}$

where R₁ and R_(i) (i=2 . . . 5) represent the vascular and avascularregions (Table 1) in the eyeball, respectively; k_(i), k_(s) and k_(b)are the thermal conductivities of the avascular tissue (in R_(i), i=2 .. . 5), vascular tissue (in R_(I)) and blood, respectively; φ is theporosity of R₁; T_(b) and T_(s) are the temperature of the blood andtissue in R₁, respectively; T_(i) is the temperature of the avasculartissue in R_(i) (i=2 . . . 5); h_(tb) is the convective heat transfercoefficient between blood and tissue structure; a_(tb) is the specificsurface area; Q_(m) is the volumetric heat generation rates due tometabolism; ρ_(s), c_(p) _(s) and σ_(b), c_(p) _(b) are the densitiesand specific heats of the tissue and blood in R₁, respectively; ρ_(i)and c_(p) _(i) are the densities and specific heats of the avasculartissue in R_(i) (i=2 . . . 5), respectively; and {right arrow over(v)}_(b) is the blood flow velocity.

The governing equations are simplified by assuming steady state. For thevascular region, the two energy equations are coupled by the convectiveheat transfer term, h_(tb) a_(tb) (T_(b)−T_(s)):

∇·(φk _(b) ∇T _(b))+∇·((1−φ)k _(s) ∇T _(s))−φρ_(b) c _(p) _(b) {rightarrow over (v)} _(b) ·∇T _(b)+(1−φ)Q _(m)=0, in R ₁  (4)

The above equation may be further simplified by assuming the capillaryvessels within the vascular tissue are thermally insignificant; meaning,there is no temperature difference between tissue and blood, i.e.T_(s)=T_(b), leading to:

{right arrow over (v)} _(b) ·∇T _(b)≈ω_(b)(T _(s) −T _(b))=0 in R ₁  (5)

where ω_(b) is the perfusion rate of blood, defined as volume flow rateof blood per unit volume of the vascular tissue, inmL-blood/[(mL-tissue)-sec]. The temperatures T_(s) and T_(b)collectively are represented as T₁ (T_(s)=T_(b)=T₁). The vascularequation can then be represented as:

∇·((φk _(b) ∇T ₁)+∇·((1−φ)k _(s) ∇T ₁)−(1−φ)Q _(m)=0, in R ₁  (6)

∇·(∇T ₁(φk _(b)+(1−φ)k _(s)))−(1−φ)Q _(m)=0, in R ₁  (7)

k _(eff) =φk _(b)+(1−φ)k _(s) and Q _(eff)=(1−φ)Q _(m)  (8)

∇·(k _(eff) ∇T ₁)−Q _(eff)=0, in R ₁  (9)

where k_(eff) is the effective value of the thermal conductivity of eyetissue and Q_(eff) is the effective volumetric heat generation rate dueto metabolism

The avascular region 520, 530, 540, 550 may be expressed as:

∇·(k ₁ ∇T _(i))=0, in R _(i) i=2 . . . 5  (10)

Table 2 shows the design parameters considered in the eye model.Although some of the parameters, such as convective heat transfercoefficient of the blood, porosity, and emissivity, are assumed to beconstant, the ambient temperature, convective heat transfer coefficientof the air are expected to vary with the environmental conditions. Theparameter values shown in Table 2 are designed to represent eye model ina controlled indoor environment.

TABLE 2 Values of parameters used in eye model ParameterDescription/Unit Value h_(∞) Convective heat transfer coefficient  10 ±2.5 between the tear film and the surrounding air [W/m²-K]* h_(b)Convective heat transfer coefficient 110 ± 10  between the vascularregion (R₁) and the surrounding blood [W/m²-K] σ Stefan Boltzmannconstant [W/m²-K4] 5.67 × 10⁻⁸ ϵ Emissivity 0.975 ± 0.021 E_(v) Tearevaporative heat flux [W/m²]*  40 ± 2.0 T_(∞) Ambient temperature [°C.]*  23 ± 1.0 φ Porosity of the healthy vascular tissue  0.3 ± 0.03Q_(m) Metabolic heat generation [W/m³] *Subject to change based on theenvironmental condition

Combination the vascular and avascular equations will provide themathematical formulation necessary for solving the core body temperatureas the boundary condition of the sclera surface that is not exposed tothe surrounding air.

∇·(k _(eff) ∇T ₁)·∇·(k _(i) ∇T _(i))−Q _(eff)=0, in R _(i) i=2 . . .5  (11)

The boundary condition for the vascular surface of the sclera notexposed to the surrounding air 610 (See FIGS. 6A-6B), Γ₁ is:

$\begin{matrix}{{{{- k_{eff}}\frac{\partial T_{1}}{\partial n_{1}}} = {h_{b}\left( {T_{1} - T_{d\; \_ \; {core}}} \right)}},{{on}\mspace{14mu} \Gamma_{1}}} & (12)\end{matrix}$

where h_(b) is the convective heat transfer coefficient between thevascular region 510 (R₁) and the surrounding blood, and

$\frac{\partial T_{1}}{\partial n_{1}}$

is me vascular temperature gradient in the direction of outward unitvector (n₁) normal to Γ₁ of R₁. T_(d_core) is the default core bodytemperature and T₁ is the vascular tissue temperature distribution ofR₁.

The boundary condition for the vascular surface of the sclera exposed tothe surrounding air 620, Γ₂ is:

$\begin{matrix}{{{{- k_{eff}}\frac{\partial T_{1}}{\partial n_{1}}} = {{h_{\infty}\left( {T_{1} - T_{\infty}} \right)} + {\sigma {ɛ\left( {T_{1}^{4} - T_{\infty}^{4}} \right)}} + E_{v}}},{{on}\mspace{14mu} \Gamma_{2}}} & (13)\end{matrix}$

The vascular surface 620 is subjected to both radiative and convectiveheat transfer, as well as evaporation from the tear film to thesurrounding air.

$\frac{\partial T_{1}}{\partial n_{1}}$

is me vascular temperature gradient in the direction of outward unitvector (n₁) normal to Γ₂ of R₁, h_(∞) is the convective heat transfercoefficient between the tear film and the surrounding air, σ is theStefan-Boltzmann constant, ε is the ocular surface emissivity, T_(∞) isthe ambient air temperature, E_(v) is the tear evaporative heat flux.Values of the parameters used in the above equations, including thethermophysical properties, are summarized in Tables 1 and 2.

The interfacial conditions between two contiguous regions are describedby the continuity condition:

$\begin{matrix}{\left. \begin{matrix}{{k_{eff}\frac{\partial T_{1}}{\partial n_{1}}} = {{- k_{i}}\frac{\partial T_{i}}{\partial n_{i}}}} \\{T_{1} = T_{i}}\end{matrix} \right),{{{on}\mspace{14mu} {IR}_{1i}\mspace{14mu} i} = {2\mspace{14mu} \ldots \mspace{14mu} 5}}} & (14)\end{matrix}$

where IR_(1i) is the interface between the vascular region R₁ and theneighboring avascular regions R_(i) (i=2 . . . 5); k_(i) and T_(i) arethe thermal conductivity and the temperature distribution of R_(i) (i=2. . . 5), respectively.

The boundary condition avascular surface 630 of the cornea Γ₃ (FIGS.6A-6B) is:

$\begin{matrix}{{{{- k_{3}}\frac{\partial T_{3}}{\partial n_{3}}} = {{h_{\infty}\left( {T_{3} - T_{\infty}} \right)} + {\sigma {ɛ\left( {T_{3}^{4} - T_{\infty}^{4}} \right)}} + E_{v}}},{{on}\mspace{14mu} \Gamma_{3}}} & (15)\end{matrix}$

where k₃ and T₃ are the thermal conductivity and temperature of thecornea tissue of the avascular region R₂, respectively,

$\frac{\partial T_{3}}{\partial n_{3}}$

is the avascular temperature gradient in the direction of outward unitvector (n₃) normal to Γ₃ of R₂.

$\begin{matrix}{{{\int\limits_{R}{\left( {k_{eff} + k_{i}} \right){{\nabla w} \cdot {\nabla{TdR}}}}} + {\int\limits_{\Gamma_{u} = {\Gamma_{2}\bigcup\Gamma_{3}}}{{w\left\lbrack {{h_{\infty}\left( {T - T_{\infty}} \right)} + {ɛ\left( {T^{4} - T_{\infty}^{4}} \right)} + E_{v}} \right\rbrack}d\Gamma_{u}}} + {\int\limits_{\Gamma_{1}}{w{h_{b}\left( {T - T_{d\; \_ \; {core}}} \right)}d\Gamma_{1}}} - {\int\limits_{R}{wQ_{eff}dR}}} = {{0\mspace{11mu} {\forall{w \in {H^{1}\mspace{11mu} i}}}} = {2\mspace{11mu} \ldots \mspace{11mu} 5}}} & (19)\end{matrix}$

where the eye domain R∪

^(d) the unknown temperature of the tissue T∈C^(n) (R) (where C^(n) is acontinuous function of n derivatives), and a test function w such thatw∈C^(n)(R). Equation 19 is the final mathematical model that estimatesthe core body temperature.

In some embodiments, an approximate solution to this mathematical modelis computed numerically using techniques that may include fixed-pointiteration, Newton's method, or a quasi-Newton method for handling thenonlinear radiative term, and techniques that may include direct solversor preconditioned iterative solvers for systems of linear equations.

In step 370, the temperature data may be transitioned from their pixelposition in the ocular surface thermal image 260 to correspondingCartesian coordinates 410 (see FIG. 4A) of a finite element mesh 400 ofthe eye model or another discretized model of the eye's geometry. Theuse of a Cartesian coordinate set is exemplary and illustrative only, asother coordinate systems may be used as would be understood by a personof ordinary skill in the art. In some embodiments, the transition may beperformed using the Equation 20 for mapping:

$\begin{matrix}{{Y_{cor} = {1 + \frac{\left( {\left( {P_{y} - Y_{\min}} \right)*\left( {N_{col} - 1} \right)} \right)}{Y_{\max} - Y_{\min}}}}{Z_{cor} = {1 + \frac{\left( {\left( {P_{Z} - Z_{\min}} \right)*\left( {N_{row} - 1} \right)} \right)}{Z_{\max} - Z_{\min}}}}} & (20)\end{matrix}$

where N_(col) and N_(row) are the column and row numbers, respectively;P_(y) and P_(z) are the pixel locations in the column and row locations,respectively; Y_(min) is the least-valued point of the y axis from thesensor data of the ocular surface; Y_(max) is the most-valued point;Z_(min) is the least-valued point of the z axis from the sensor datapoint of the ocular surface; Z_(max) is the most-value point of the zaxis from the sensor data point of the ocular surface; and Y_(cor) andZ_(cor) are the sensor locations in the eye model corresponding to theP_(y) and P_(z) pixels of the ocular surface thermal image 260.

Zero or missing values may be validated. Once the temperature values aremapped from the 2D of the thermal image to 3D sensor data points of theocular surface of the eye model 400, the eye model 400 may beelectronically stored as an observed input value that may be used toestimate the temperature at the back of the eye using inverse analysisand optimization. In some embodiments, models of heat transfer may beused to map between core temperature and temperatures on the ocularsurface.

In step 380, the temperature at the back of the eye is estimated usingthe eye model 400. The estimate may be obtained using a gradient-basedor non-gradient-based optimization procedure to estimate the core bodytemperature at the back of the eye that produces the ocular surfacetemperature profile that best fits the data according to some meritfunction. For the temperature estimation in step 380, the temperaturedata may be evaluated using a combination of forward and backwardmethods, otherwise known as inverse analysis. In one embodiment, themathematical formulations of the eye model which may include a governingequation, formulated in Equation. 19, along with the goodness of fittest and non-gradient optimization are used to evaluate the surfacetemperature at the back of the eye. The inverse problem may be set up asa minimization function of temperature (T), where the analysis can beperformed by iterative minimization of an object function. As an initialstarting point, guess the value of T at the surface boundary of Γ₁ andsolve the ocular surface temperature T at the surface boundary of Γ₂ andΓ₃ using a forward method. The estimated temperature data of the ocularsurface (i.e. T at Γ₂ and Γ₃) may then undergo the goodness of fit testwith the ocular surface temperature data obtained from the infraredcamera where the convergence to the minimum of the objective function isassessed. Depending on the result of the fit, the initial guess may thenbe updated, and a new estimate of ocular surface temperature isevaluated. The iterative process continue until the objective functionis satisfied, i.e. best core body temperature value is attained. Tohandle the iterative process, non-gradient-based optimization may beperformed using Brent's method, golden section search method, downhillsimplex, or a pattern search method; alternatively, a gradient-basedtechnique such as steepest descent, conjugate gradient, theBroyden-Fletcher-Powell-Reeves method, or Newton's method may be used.The chi-square test may be used to assess the goodness of fit testbetween the estimated and infrared measured ocular surface temperaturedata.

Equation 21 shows formulation of the reduced chi-square (χ_(red) ²)equation, in which χ_(red) ² is given by:

$\begin{matrix}{\chi_{red}^{2} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\left( \frac{{T_{IR}\left( {r_{i};\alpha} \right)} - T_{i}}{\varrho (T)} \right)^{2}}}} & (21)\end{matrix}$

where T_(IR) represents the ocular surface temperature acquired from thethermal image; T_(i) (where i=1 and 3) represents the estimated ocularsurface temperature evaluated using Equation 19; r is the position ofthe temperature sensors, a is the optimization parameter described as afunction of the core body temperature; and N is the total number ofsensors located on the ocular surface area of the eye model. HereinT_(IR)(r; α) is fitted to N number of numerically generated ocularsurface temperature data (T_(i)). Since χ_(red) ² is formulated toaccount the noise inherited from the instrumentation error,

(T) is added to account for the noise equivalence difference temperatureof the camera provided by the manufacturer. It should be noted that,since

(T) is uniform across the image, the method produces a core bodytemperature estimate that is independent of the accuracy rating of thecamera.

For a single model assessment, the accuracy of the fitness isestablished based on the following criteria:

-   -   λ_(red) ²>1—Poor fit.    -   λ_(red) ²≈1—Good fit.    -   λ_(red) ²<1—Over fit.

In step 390, the estimated core body temperature and (optionally) themodel 400 may be transmitted to the output device 140.

FIGS. 4A-4B show diagrams of temperature data being applied a model ofthe eye. In FIG. 4A, the thermal image of the right eye 260 r isconverted into coordinates 410 which relate to the finite element mesh400. In FIG. 4B, the thermal image of the right eye 260 r is shown beingmapped to the mesh 400 which is used to form the eye model 420 with aback of the eye 430.

While embodiments in the present disclosure have been described in somedetail, according to the preferred embodiments illustrated above, it isnot meant to be limiting to modifications such as would be obvious tothose skilled in the art.

The foregoing disclosure and description of the disclosure areillustrative and explanatory thereof, and various changes in the detailsof the illustrated apparatus and system, and the construction and themethod of operation may be made without departing from the spirit of thedisclosure.

What is claimed is:
 1. An infrared temperature estimating methodcomprising: transitioning temperature data from a thermal image of anocular surface of an eye to an ocular surface of a model of the eye; andestimating a core body temperature at the back of the model of the eye.2. The method of claim 1, further comprising: transmitting the estimatedcore body temperature to an output device.
 3. The method of claim 1,further comprising: obtaining the thermal image of the ocular surface ofthe eye; and extracting the temperature data from the thermal image ofthe ocular surface using a processor.
 4. The method of claim 3, furthercomprising: detecting at least part of a facial surface comprising theocular surface of the eye; acquiring a facial thermal image of the atleast part of the facial surface; and transmitting the facial thermalimage to the processor, where the facial thermal image comprises thethermal image of the ocular surface of the eye.
 5. The method of claim1, where the step of estimating the core body temperature comprises:using at least one model of heat transfer to map between coretemperature and temperatures on the ocular surface; and performing anoptimization to estimate the core body temperature at the back of theeye.
 6. The method of claim 1, wherein the transition step comprises:applying temperature data from pixel positions of the thermal image ofthe ocular surface of the eye to an ocular surface of a discretizedmodel of the eye.
 7. The method of claim 6, wherein the discretizedmodel includes a finite element mesh.
 8. The method of claim 1, furthercomprising: constructing the model of the eye based on thermophysicalproperties and boundaries of a cornea, an anterior humor, a vitreoushumor, a lens, a retina, a choroid, an iris, a ciliary body, and asclera of an eye.
 9. The method of claim 1, where the core temperatureis estimated using the equation:${{\int\limits_{R}{\left( {k_{eff} + k_{i}} \right){{\nabla w} \cdot {\nabla{TdR}}}}} + {\int\limits_{\Gamma_{U} = {\Gamma_{2}\bigcup\Gamma_{3}}}{{w\left\lbrack {{h_{\infty}\left( {T - T_{\infty}} \right)} + {ɛ\left( {T^{4} - T_{\infty}^{4}} \right)} + E_{v}} \right\rbrack}d\Gamma_{u}}} + {\int\limits_{\Gamma_{1}}{w{h_{b}\left( {T - T_{d\; \_ \; {core}}} \right)}d\Gamma_{1}}} - {\int\limits_{R}{wQ_{eff}dR}}} = {{0\mspace{11mu} {\forall{w \in {H^{1}\mspace{14mu} i}}}} = {2\mspace{11mu} \ldots \mspace{11mu} 5}}$where k_(eff) is the effective value of the thermal conductivity of eyetissue, k_(i) is the thermal conductivity of eye tissue in region i, wis the test function such that w∈C^(n)(R) (C^(n) is a continuousfunction of n derivatives and R is the eye domain such that R∪

^(d)), Γ₁ is part of the eye surface that is not exposed to thesurrounding air, and Γ₂∪Γ₃ is part of the eye surface that is exposed tothe surrounding air, T is the ocular surface temperature at Γ₂∪Γ₃ andthe estimated core body temperature (the surface temperature at the backof the eye) at Γ₁, T_(∞) is ambient temperature, ε is emissivity, E_(v)is tear evaporative heat flux, Q_(eff) is the effective volumetric heatgeneration rate due to metabolism, T_(d_core) is the default core bodytemperature (typically set by the user), h_(∞) is convective heattransfer coefficient between the tear film and the surrounding air, andh_(b) is the convective heat transfer coefficient between the vascularregion (R₁) and the surrounding blood.
 10. A system for estimating acore body temperature, comprising: a non-transitory computer-readablemedium in communication with a processor and comprising a program that,when executed, performs a method, the method comprising: transitioningtemperature data from a thermal image of an ocular surface of an eye tothe ocular surface of a model of the eye; and estimating the core bodytemperature at the back of the eye model.
 11. The system of claim 10,wherein the model of the eye is based on thermophysical properties andboundaries of a cornea, an anterior humor, a vitreous humor, a lens, aretina, a choroid, an iris, a ciliary body, and a sclera of an eye. 12.The system of claim 10, further comprising: an infrared camera incommunication with the processor.
 13. The system of claim 10, furthercomprising: an output device in communication with the processor.